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dengan menggunakan metode horner carilah hasil bagi dan sisa bagi dari setiap pembagian p(x) oleh q(x) berikut p(x)=x⁵-2x³+7x-1 dan q(x)=x+2

To solve the problem using **Horner's method**, we need to perform synthetic division on the polynomial \( P(x) = x^5 - 2x^3 + 7x - 1 \) by \( Q(x) = x + 2 \).

**Step-by-Step Solution:**

### Step 1: Setting up the division.
- First, express the divisor \( Q(x) = x + 2 \) in the form \( x - c \). Here, \( c = -2 \).
- The coefficients of \( P(x) = x^5 - 2x^3 + 7x - 1 \) are: \([1, 0, -2, 0, 7, -1]\), where the zero coefficients correspond to missing terms.

### Step 2: Synthetic division setup.
We will use synthetic division with \( c = -2 \) on the coefficients \([1, 0, -2, 0, 7, -1]\).

Let's perform the calculation.The result of dividing \( P(x) = x^5 - 2x^3 + 7x - 1 \) by \( Q(x) = x + 2 \) using Horner's method is:

- **Quotient**: \( x^4 - 2x^3 + 2x^2 - 4x + 15 \)
- **Remainder**: \( -31 \)

Would you like further clarification on any step? Here are some additional related questions:

1. How does synthetic division differ from long division of polynomials?
2. Can we always use Horner's method for any polynomial division?
3. How do we interpret the remainder in polynomial division?
4. What happens if the remainder is zero after the division?
5. Can synthetic division be used for non-linear divisors?

**Tip:** Horner's method is particularly efficient for evaluating polynomials at specific points, not just for division.

Dengan menggunakan Metode Horner, carilah hasil bagi dan sisa dari setiap pembagian P(x) oleh Q(x) berikut P(x) = x⁵ - 2x³ + 7x - 1 dan Q(x) = x + 2

Learn how to use Horner's method to solve the polynomial division P(x) = x⁵ - 2x³ + 7x - 1 divided by Q(x) = x + 2. This step-by-step guide covers key algebraic concepts, synthetic division, and remainder calculation. Suitable for high school students in Grades 10-12.

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